Datums and map projections for remote sensing, GIS and surveying

A practical guide to coordinate reference systems, Datums and Map Projections: For Remote Sensing, GIS and Surveying has become a key book for many students and professionals around the world. While retaining the benefits of the first edition - clear presentation assuming no prior knowledge, a problem-solving approach, practical examples and the combination of GPS-derived data from other sources - the rewritten and expanded second edition includes a revised structure that better groups common themes, greater scope and coverage of all possible types of coordinate reference systems, more examples and case studies from around the world, terminology of the ISO 1911, and color illustrations.

Preface	p. ix
Chapter 1 Introduction	p. 1
1.1 The context	p. 1
1.2 Introduction to the concepts and the structure of this book	p. 2
Chapter 2 Coordinates and reference systems	p. 8
2.1 The Earth - geoid and ellipsoid	p. 8
2.1.1 The geoid	p. 8
2.1.2 Models of the shape of the Earth - the ellipsoid	p. 8
2.2 Coordinate systems	p. 11
2.2.1 Coordinate system attributes	p. 11
2.2.2 Coordinate systems for the sphere and ellipsoid	p. 12
2.2.3 Geocentric Cartesian coordinates	p. 14
2.2.4 Conversion between ellipsoidal and geocentric Cartesian coordinates	p. 15
2.2.5 Map projection coordinates	p. 16
2.2.6 Cartesian coordinates for engineering applications	p. 17
2.2.7 Gravity-related systems (height and depth)	p. 18
2.2.8 Miscellaneous coordinate systems	p. 19
2.3 Datums and coordinate reference systems	p. 20
2.3.1 Datum overview and classification	p. 20
2.3.2 Geodetic datums and coordinate reference systems	p. 20
2.3.3 Projected coordinate reference systems	p. 28
2.3.4 Vertical systems	p. 29
2.3.5 Engineering datums and coordinate reference systems	p. 35
2.3.6 Image datums and coordinate reference systems	p. 35
2.4 Compound coordinate reference systems	p. 36
2.5 Coordinate reference system identification	p. 36
2.5.1 CRS description	p. 36
2.5.2 Registers of coordinate reference systems	p. 38
Chapter 3 Map Projections	p. 39
3.1 Introduction	p. 39
3.2 Map projections: fundamental concepts	p. 40
3.2.1 Grids and graticules	p. 40
3.2.2 Scale factor	p. 40
3.2.3 Developable surfaces	p. 42
3.2.4 Preserved features	p. 44
3.2.5 Spheres and ellipsoids	p. 46
3.3 Cylindrical projections	p. 48
3.3.1 Cylindrical equidistant	p. 48
3.3.2 Cylindrical equal area	p. 51
3.3.3 The Mercator projection	p. 53
3.3.4 Transverse Mercator	p. 55
3.3.5 South-oriented Transverse Mercator	p. 61
3.3.6 Oblique Mercator	p. 61
3.4 Azimuthal projections	p. 63
3.4.1 General azimuthal	p. 63
3.4.2 Azimuthal equidistant	p. 63
3.4.3 Azimuthal equal area	p. 64
3.4.4 Stereographic	p. 66
3.4.5 Gnomonic	p. 69
3.4.6 Azimuthal orthographic	p. 70
3.4.7 Azimuthal perspective projection	p. 70
3.5 Conic projections	p. 73
3.5.1 General conic	p. 73
3.5.2 Conic equidistant	p. 75
3.5.3 Albers equal area	p. 75
3.5.4 Lambert Conformal Conic	p. 77
3.5.5 Oblique conic	p. 79
3.6 Non-geometric projection methods	p. 80
3.7 Summary of information required	p. 83
3.7.1 Map projection method formulae	p. 83
3.7.2 Map projection parameter values	p. 84
3.8 Computations within map projections	p. 86
3.9 Designing a map projection	p. 89
Chapter 4 Transformations	p. 90
4.1 Introduction	p. 90
4.2 General characteristics of transformations	p. 91
4.2.1 Transformations and conversions	p. 91
4.2.2 Transformation multiplicity	p. 91
4.2.3 Transformation accuracy	p. 92
4.2.4 Transformation reversibility	p. 93
4.3 Transformations between geocentric coordinate reference systems	p. 93
4.3.1 Introduction	p. 93
4.3.2 Three parameter geocentric transformation	p. 94
4.3.3 Seven parameter geocentric transformation	p. 95
4.3.4 Ten parameter geocentric transformation	p. 98
4.4 Transformations between geographic coordinate reference systems	p. 100
4.4.1 Introduction	p. 101
4.4.2 Molodensky and Abridged Molodensky	p. 101
4.4.3 Geographic offsets	p. 102
4.4.4 Grid interpolation - NTv2 and NADCON	p. 104
4.4.5 Indirect transformation between geographic coordinate reference systems	p. 106
4.5 Transformation of 2D plane coordinates	p. 109
4.5.1 Introduction	p. 109
4.5.2 Compatibility of coordinate reference systems	p. 110
4.5.3 Similarity transformation method	p. 113
4.5.4 Affine transformation	p. 115
4.5.5 Polynomials	p. 117
4.5.6 Creating overlays in Google Earth	p. 118
4.5.7 Transformation of GPS data onto a local site grid	p. 120
4.5.8 Indirect transformations between projected coordinates	p. 122
4.6 Coordinate operations for vertical coordinate reference systems	p. 123
4.6.1 Introduction	p. 123
4.6.2 Vertical offsets	p. 124
4.6.3 The hub concept	p. 127
4.7 Transformation between ellipsoidal and gravity-related heights	p. 128
4.7.1 Geoid models	p. 128
4.7.2 Height correction models	p. 129
4.7.3 Transformations involving compound coordinate reference systems (CRSs)	p. 130
4.8 Selecting a transformation	p. 131
4.8.1 Introduction	p. 131
4.8.2 Officially sanctioned transformations	p. 132
4.8.3 Selecting from a transformation repository	p. 132
4.9 Deriving your own transformation	p. 134
4.9.1 Introduction	p. 134
4.9.2 Choice of transformation method	p. 134
4.9.3 Availability of control points	p. 135
4.9.4 Geometric issues	p. 136
4.9.5 Effect of ignoring geoid-ellipsoid separation	p. 137
4.9.6 Evaluating results of the transformation	p. 140
Chapter 5 Global Navigation Satellite Systems	p. 141
5.1 Introduction	p. 141
5.2 The systems	p. 141
5.3 Positioning with codes	p. 143
5.4 Differential GNSS and augmentation systems	p. 146
5.5 GNSS measurements using phase observations	p. 148
5.6 Coordinate reference system considerations	p. 152
Chapter 6 Case Studies	p. 154
6.1 Transformation of GPS data into a local coordinate reference system	p. 154
6.2 Creation of a three-parameter geocentric transformation from an official national transformation	p. 160
6.3 Designing a map projection	p. 162
6.4 Calculations using map grid coordinates	p. 164
6.5 Creating overlays in Google Earth	p. 172
Appendix A Terminology	p. 176
Appendix B Computations with spherical coordinates	p. 181
Appendix C Basic geometry of the ellipsoid	p. 182
C.1 Introduction	p. 182
C.2 Radii of curvature of the ellipsoid	p. 182
C.3 Normal sections and geodesics	p. 182
C.4 Forward computation of coordinates	p. 184
C.5 Reverse computation of azimuth	p. 184
C.6 Determination of points on the geodesic	p. 185
Appendix D The Molodensky equations	p. 186
Appendix E Determination of transformation parameter values by least squares	p. 187
E.1 Introduction and least squares terminology	p. 187
E.2 Two dimensional transformations of Cartesian coordinates	p. 189
E.2.1 The Similarity transformation	p. 189
E.2.2 The affine transformation	p. 192
E.2.3 Second order polynomials	p. 193
E.3 Three-dimensional transformations of Cartesian coordinates	p. 194
E.3.1 The seven-parameter transformation	p. 194
E.3.2 The ten-parameter geocentric transformation	p. 196
E.3.3 Subsets of the seven-parameter geocentric transformation	p. 196
E.4 Worked example	p. 197
References & Further Reading	p. 200
Index	p. 203

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